class mrpt::math::CSparseMatrix::CholeskyDecomp

Auxiliary class to hold the results of a Cholesky factorization of a sparse matrix.

This implementation does not allow updating/downdating.

Usage example:

CSparseMatrix  SM(100,100);
SM.insert_entry(i,j, val); ...
SM.compressFromTriplet();

// Do Cholesky decomposition:
   CSparseMatrix::CholeskyDecomp  CD(SM);
CD.get_inverse();
...

Only the upper triangular part of the input matrix is accessed.

This class was initially adapted from “robotvision”, by Hauke Strasdat, Steven Lovegrove and Andrew J. Davison. See http://www.openslam.org/robotvision.html

This class designed to be “uncopiable”.

See also:

The main class: CSparseMatrix

#include <mrpt/math/CSparseMatrix.h>

class CholeskyDecomp
{
public:
    // construction

    CholeskyDecomp(const CSparseMatrix& A);
    CholeskyDecomp(const CholeskyDecomp& A);

    //
methods

    CholeskyDecomp& operator = (const CholeskyDecomp&);
    CMatrixDouble get_L() const;
    void get_L(CMatrixDouble& out_L) const;

    template <class VECTOR>
    VECTOR backsub(const VECTOR& b) const;

    void backsub(const CVectorDouble& b, CVectorDouble& result_x) const;
    void backsub(const double* b, double* result, const size_t N) const;
    void update(const CSparseMatrix& new_SM);
};

Construction

CholeskyDecomp(const CSparseMatrix& A)

Constructor from a square definite-positive sparse matrix A, which can be use to solve Ax=b The actual Cholesky decomposition takes places in this constructor.

Constructor from a square semidefinite-positive sparse matrix.

Only the upper triangular part of the matrix is accessed.

The actual Cholesky decomposition takes places in this constructor.

Parameters:

std::runtime_error	On non-square input matrix.
mrpt::math::CExceptionNotDefPos	On non-definite-positive matrix as input.
std::runtime_error	On non-square input matrix.
mrpt::math::CExceptionNotDefPos	On non-semidefinite-positive matrix as input.

Methods

CMatrixDouble get_L() const

Return the L matrix (L*L’ = M), as a dense matrix.

void get_L(CMatrixDouble& out_L) const

Return the L matrix (L*L’ = M), as a dense matrix.

template <class VECTOR>
VECTOR backsub(const VECTOR& b) const

Return the vector from a back-substitution step that solves: Ux=b.

void backsub(const CVectorDouble& b, CVectorDouble& result_x) const

Return the vector from a back-substitution step that solves: Ux=b.

Vectors can be Eigen::VectorXd or mrpt::math::CVectorDouble

void backsub(const double* b, double* result, const size_t N) const

overload for double pointers which assume the user has reserved the output memory for result

Return the vector from a back-substitution step that solves: Ux=b.

void update(const CSparseMatrix& new_SM)

Update the Cholesky factorization from an updated vesion of the original input, square definite-positive sparse matrix.

NOTE: This new matrix MUST HAVE exactly the same sparse structure than the original one.